That’s a bit of a tricky question, because it’s math-heavy. The best way to describe it is to think of the event horizon as the black hole, and forget that there is even an interior. The black hole can be fully described by the conditions at the event horizon after all, and everything else is cut off from the surrounding universe completely. In that sense there is no propagation from the interior at all, which is good because if information could escape then theories describing black holes would be broken.
Instead the black hole has mass, charge, and momentum (three kinds of momentum actually, but that’s not important). Whatever is going on beyond the event horizon, whatever that might be, has no effect that anyone can detect. Matter is accreted “onto” the event horizon which then expands in proportion to the mass of the volume of the hole. Maybe it’s destroyed beyond that point, or maybe it goes to another universe, but we can never know. The event horizon can also shrink if the surroundings are sufficiently cold (really really really cold) and the horizon is sufficiently hot.
Still, all of this is surface phenomena, like dropping a bowling ball into a tub of water. The water only “knows” about the surface of the ball, which which gets properties from the whole ball without exposing the center. A bowling ball in water creates waves, but the interior isn’t interacting with the water anymore than the black hole interior interacts with space (assuming an idealized perfectly rigid bowling ball). In the same way gravity waves or fractions would be a function of how the space just beyond the event horizon is warped.
Does that help?